Uncertainty Analysis for Photovoltaic Degradation Rates

D.C. Jordan1, S.R. Kurtz1, C. Hansen2

1National Renewable Energy Laboratory, Golden, CO 80401, USA 

2Sandia National Laboratories, P.O. Box 5800 Albuquerque, New Mexico 87185-1033

Introduction

NREL PV Module Reliability Workshop, Golden CO, Feb.25-26, 2014 • NREL/PO-5200-61449

Irradiance Source Strategies 

Ishikawa Diagram Intentionally Drifting Pyranometer

Conclusion

Uncertainty for “Clean” Data Set

With a “clean” data set Rd can be determined to within 

0.2%/year after 4 years of field data

Total Uncertainty Simulation

Long-term PV Performance

1. Financially: 

Cash flow

Uncertainty directly related to risk

2. Technically: 

Lifetime prediction

Product improvement

Drift Occurrence 

1

3

2

4

6

5

7

8

9

Sources of variations & strategies for degradation rate uncertainty 

Apparent high “Rd” due to drifting pyranometer

CM10 pyranometer (high humidity) drifted about 1%/year

Condensation film on dome

Precision (relative accuracy) more important than 

absolute accuracy

 Seasonality caused by temperature, angle-of-incidence, spectral 

effects can lead to systematic errors and higher uncertainties

 Temperature-corrected metrics are preferred over non-corrected 

metrics.

 Changes (drift) of instrumentation during field exposure is more critical 

than absolute accuracy

 Drift has significantly more impact at the end of the monitoring period 

than in the middle

 Nearby irradiance sensors may be used to determine degradation 

rate

Pyranom. Rd 

(%/year)

Uncertainty 

(%/year)

Regular -0.18 0.38

High 

humidity -1.15 0.36

Median(DC/POA

unadjusted)

Rd=-0.21+/-0.16 (%/year) Rd=-0.22+/-0.02 (%/year)

1 All 9 years st 4 years

1

1.1

1.2

1.3

1.4

DC/POAcorr Tamb D

0 1000 2000 3000

Day

Multi-Si 1400kW system at NREL

Rd=-0.30 %/year

Median of 10 pyranometers at OTF

Pyranometer mounted 

on system

Rd=-0.15 %/year

Precision pyranometer,

1⁄4 km distant

Rd=-0.28 %/year

Rd

Rd SE

RMIS: OTF weather 

station

Rd=-0.33 %/year

DCPOAcorr

Rd

Rd SE

Rd

Rd SE

Rd

Rd SE

Using Irradiance from nearby system may be adequate

Instrumenting every system with pyranometer may not be necessary

Instrumentation Uncertainties

1R. Faranda, S. Leva, WSEAS Transactions on Power Systems, 2010.

2M. B. Strobel et al.,Solar Energy Materials & Solar Cells 93 (2009) 1124–1128.

3D.R. Myers et al., 2004, NREL Conference Paper NREL/CP-560-36320. 4H. Müllejans et al., Meas. Sci.Technol. 20 (2009) 075101. 5D.C. Jordan et al., NREL PVMR Workshop, Golden CO, USA, 2013.

6N.H. Reich et al., PVSC, Austin, TX, 2012, 1551 – 1555. 7http://www.solarabcs.org/

Even a small drift dominates 

other uncertainties

Whitfield et al., PiPV 2001.

Belts et al., PVSEC 2005.

Dominé et al., PVSEC, 2010.

Kiefer, PVSEC, 2010

Kimber, PVSC, 2009

Jordan et al., PVSC, 2013

Jordan et al., PVSC, 2010

Jordan, PVMR workshop, 2010.

Kurtz et al., NREL report, 2013

Jordan et al., PVMR, 2012.

C. Hansen, Sandia report 2013.

Reich et al., PVSC, 2012.

Jordan et al., WREF 2012.

Duck et al., PVSC 2013

Jordan et al., PVSC, 2010, Jordan et al. PVSC 2013

Hasselbrink et al., PVSC 2013

Marion, PVSC 2012

Seasonality & Metrics Monte Carlo Simulation

1. 1.4 kW multi-Si system

2. Use temperature-corrected Performance ratio (PR)

3. Use a drift of 1%/year on average (low: 0.5%/year, high: 1.5%/year, triangle distribution)

4. Let the drift have different length 1,2,3... years

5. Let the drift occur at different times of field exposure

6. 1000 realizations, calculate Rd for each realization

Need to determine degradation rates (Rd) accurately

If drift occurs during middle of field exposure negligible effect

If drift occurs at end of field exposure  may have large effect

Y

PR=Performance Ratio

E=Net Energy output

P0=Nameplate DC 

rating 

H=In-plane Irradiance

G=Reference Irradiation

GH

P

E

PR 0 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50

Performance Ratio (%)

Time (Months)

Trough‐to‐crest, Rd=‐0.6 (%/year)

Crest‐to‐crest, Rd=‐1.1 (%/Year)

Crest‐to‐trough, Rd=‐1.9 (%/year)

Seasonality can lead to 

systematic deviations

Temp-corrected metrics: excellent 

agreement down to 3 1⁄2 years.

Seasonality Metrics

DC/GPOA: DC power/ plane-of-array Irradiance

DC/GPOAcorr: temperature-corrected DC/GPOA

PR: Performance ratio

Prcorr: temperature-corrected PR

PVUSA: PVUSA regression methodology

Temperature-corrected metrics are preferred over noncorrected metrics.

Uncertainties are only statistical uncertainty and do not include instrumentation